Circuit and device nonlinearities are well known in the art to create undesired intermodulation distortion. In many applications, these nonlinearities and associated intermodulation distortion of circuits and devices limit the performance of systems and often lead to designs with increased power consumption in efforts to avoid intermodulation distortion. Example applications include the receiver and transmitter portions of cellular phone handsets, base stations, cable television head-ends, cable television amplifiers, and general purpose amplifiers. In receivers, the presence of strong undesired signals, typically at nearby frequencies, can produce intermodulation products that interfere with the reception of weak desired signals. In transmitters, intermodulation distortion can lead to the generation of undesired frequency emissions that violate regulatory requirements and interfere with other services, typically at nearby frequencies.
For example, in cellular phones the problem of receiving weak signals in the presence of strong signals is of considerable interest. It is common for a cellular phone to be situated far from a base-station antenna tower (leading to a weak desired signal from the tower) while other strong signals such as nearby cellular phones, television transmitters, radar and other radio signals interfere with the reception of the desired weak signal. This interference is further exacerbated by nonlinearities within electronic circuits, including third order nonlinearities that are well known in the art to limit the performance of circuits and devices.
In addition to the problems created by nonlinearities in radio receivers, radio transmitters are similarly affected by third-order and other nonlinearities. Such nonlinearities in transmitters lead to undesired transmitter power in frequency bands outside the desired transmission frequency bands, such effects being commonly referred to as spectral re-growth in the art. These out-of-band signals in radio transmitters can violate regulatory emission requirements and cause interference with other users operating at nearby frequencies.
In broadband systems, such as cable television, nonlinearities present particular problems since such systems have a plurality of signals (i.e., television signals) at relatively high power levels. This plurality of signals, combined with relatively high power levels, can lead to particular sensitivity to channel-to-channel interference problems induced by nonlinearities in broadband and cable television applications.
In addition, it is well known in the art that nonlinearities are also used in: a beneficial manner to achieve desired effects, and in such cases enhancement of the nonlinearities is the desired outcome. Example applications where such enhancement of nonlinearities is desirable are harmonic mixers and frequency multipliers.
The nonlinearities of devices, such as amplifiers, are commonly modeled as Taylor series expansions, i.e., power series expansions or polynomial expansions, of an input signal. For example, the output voltage y of a device may be described as a Taylor series, or polynomial, expansion of the input voltage x:y=a0+a1x+a2x2+a3x3+ . . .                 where a0, a1, a2, a3 . . . are constants representative of the behavior of the particular device being modeled, and the order of the polynomial is determined by the highest power of x in the polynomial expansion. In most situations, the linear term a1x is the desired linear signal, and the terms anxn, with n≠1, are undesired. The term a0 represents a constant, or DC (direct current), offset that is easily removed in most applications.        
In radio applications, the term a3x3 is particularly problematic when an input signal such as x=A cos(ω1t)+A cos(ω2t) is considered. In this case the cubic term of the Taylor series is defined as:a3x3=a3A3[cos3(ω1t)+3 cos2(ω1t)cos(ω2t)+3 cos(ω1t)cos2(ω2t)+cos3(ω2t)]where the terms cos2(ω1t)cos(ω2t) and cos(ω1t)cos2(ω2t) can be further expanded to:                                                         cos              2                        ⁡                          (                                                ω                  1                                ⁢                t                            )                                ⁢                      cos            ⁡                          (                                                ω                  2                                ⁢                t                            )                                      =                              1            4                    ⁡                      [                                          2                ⁢                                  cos                  ⁡                                      (                                                                  ω                        2                                            ⁢                      t                                        )                                                              +                              cos                ⁡                                  (                                                            2                      ⁢                                              ω                        1                                            ⁢                      t                                        +                                                                  ω                        2                                            ⁢                      t                                                        )                                            +                              cos                ⁡                                  (                                                            2                      ⁢                                              ω                        1                                            ⁢                      t                                        -                                                                  ω                        2                                            ⁢                      t                                                        )                                                      ]                                                                        cos            ⁡                          (                                                ω                  1                                ⁢                t                            )                                ⁢                                    cos              2                        ⁡                          (                                                ω                  2                                ⁢                t                            )                                      =                              1            4                    ⁡                      [                                          2                ⁢                                  cos                  ⁡                                      (                                                                  ω                        1                                            ⁢                      t                                        )                                                              +                              cos                ⁡                                  (                                                            2                      ⁢                                              ω                        2                                            ⁢                      t                                        +                                                                  ω                        1                                            ⁢                      t                                                        )                                            +                              cos                ⁡                                  (                                                            2                      ⁢                                              ω                        2                                            ⁢                      t                                        -                                                                  ω                        1                                            ⁢                      t                                                        )                                                      ]                              where the terms cos(2ω1t−ω2t)/4 and cos(2ω2t−ω1t)/4 are well known in the art to present particular difficulty in the design of communications equipment since they can produce undesired in-band distortion products at frequencies close to the desired linear signal frequencies. For example, at frequencies of f1=100 MHz and f2=100.1 MHz, with ω1=2πf1 and ω2=2πf2, the undesired frequency component 2ω1−ω2 is a frequency of 99.9 MHz and 2ω2−ω1 is a frequency of 100.2 MHz. These two undesired frequencies at 99.9 and 100.2 MHz are created by the third-order nonlinearity of the polynomial (i.e., a3x3), and are so close to the desired linear signal frequencies of 100 and 100.1 MHz that they cannot easily be removed by filtering.
One prior art approach to the problem employs feedforward compensation wherein a distortion error signal is generated by taking the difference between a first amplified and distorted signal, and a second undistorted signal, and later subtracting the distortion error signal from the first amplified and distorted signal in order to remove the distortion components.
This prior art is illustrated in the schematic drawing of FIG. 1, in which an apparatus 10 incorporating feedforward compensation is shown by way of example. An input signal 12 is applied both to first amplifier 14 and a first delay device 16. The time delay of the first delay device equals the time delay of the first amplifier. The output signal 18 of the first amplifier is attenuated by the attenuator 20. The output signal 22 of the first delay device is subtracted from the output signal 24 of the attenuator in a first subtractor 26 resulting in error signal 28. The output signal 18 of the first amplifier is also input to a second delay device 30. The time delay of the second delay device equals the time delay of the second amplifier 32 that amplifies the error signal. The output signal 34 of the second amplifier is subtracted from the output signal 36 of the second delay in a second subtractor 38 to form the final output signal 40.
For illustrative purposes, an example input frequency spectrum 42 is shown for input signal 12 comprised of two input spectral lines of equal amplitude at different frequencies. The spectrum at the output signal 18 of the first amplifier 14 is illustrated in second spectrum 44 where the two innermost spectral lines correspond to the original input frequencies illustrated in the input spectrum, but with larger amplitude, and the two outermost spectral lines representing third-order distortion components of the output signal 18 of the first amplifier. The spectrum at the error signal 28 is illustrated in third spectrum 46 where the two spectral lines correspond to an attenuated version of the third-order distortion components of the second spectrum 44 (the two outermost spectral lines in the second spectrum). In the third spectrum the attenuation of attenuator 20 has adjusted the signal to completely eliminate the two innermost spectral components of the second spectrum. The spectrum at the output signal 34 of the second amplifier 32 is illustrated in fourth spectrum 48 where the two spectral lines correspond to an amplified version of the third spectrum, where the amplitude of the spectral components in the fourth spectrum equals the amplitude of the two outermost spectral components of the second spectrum. The spectrum at the final output signal 40 is illustrated in the fifth spectrum 50 where the two spectral lines correspond to an amplified version of the input frequency spectrum and all distortion products in the second spectrum (the two outermost spectral lines in second spectrum) are canceled and eliminated.
For examples similar to the one illustrated in FIG. 1, see, U.S. Pat. No. 5,489,875, issued on Feb. 6, 1996, in the name of inventor Cavers, which describes an adaptive version of this well-known scheme, and a similar scheme is described in U.S. Pat. Nos. 5,157,346, and 5,323,119, issued on Oct. 20, 1992 and Jun. 21, 1994, respectively, in the name of inventors Powell et al. Similar approaches are disclosed in U.S. Pat. No. 4,379,994, Bauman, issued Apr. 12, 1983; U.S. Pat. No. 4,879,519, Myer, issued Nov. 7, 1989; U.S. Pat. No. 4,926,136, Olver, issued May 15, 1990; U.S. Pat. No. 5,157,346, Powell et al., issued Oct. 20, 1992; U.S. Pat. No. 5,334,946, Kenington, issued Aug. 2, 1994; and U.S. Pat. No. 5,623,227, Everline et al., issued Apr. 22, 1997.
However, these prior art approaches require delay lines, of considerable physical size, to compensate for delay through the amplifiers. These approaches also require the availability of undistorted reference signals and further rely on accurate generation of the distortion error signal. In many applications the undistorted signal may not be available or may be of such a small power level as to be unusable in prior art applications. A further disadvantage of the prior art is that said distortion error signal contains amplified noise components of the amplified and distorted signal that can degrade the noise of the overall system, making the prior art unattractive for application in low noise systems such as radio receivers. In addition, the prior art approaches relate more directly to power amplifier devices because of the aforesaid limitations. Therefore, a need exists to substantially reduce and/or cancel nonlinearities without the need for delay lines, without the need for undistorted reference signals, and without the need for a distortion error signal, such distortion error signal containing only distortion components and not containing components of the undistorted signal.
A second prior art approach to the problem employs push-pull compensation as shown in FIG. 2. As shown the apparatus 60 comprises a first hybrid splitter 62, first and second amplifiers 64, 66 and a second hybrid splitter 68 that functions as a combiner. An input signal 70 is first split into first and second coupled signals 72 and 74 by first hybrid splitter 62, wherein the second coupled signal is 180 degrees out of phase with the first coupled signal. As is well known in the art, the fourth port of both the first and second hybrid splitters are properly terminated with impedance matched terminating loads 76 and 78. The first coupled signal is input to the first amplifier 64 and the second coupled signal is input to the second amplifier 66, with the first and second amplifiers being identical. The input-output relationship of the first and second amplifier, being identical, may be approximated by a Taylor, or power, series. For illustration, let a0 be zero in the Taylor series, and consider terms up to the fourth order. Then, denote the first coupled signal 72 to the first amplifier 64 as x, and denote the first output signal 80 of the first amplifier 64 as y1. The first output signal 80 of the first amplifier 64 can then be approximated as:y1=a1x+a2x2+a3x3+a4x4 
Since the second coupled signal 74, being the input of the second amplifier 66 is 180 degrees out of phase with the first coupled signal 72 of the first amplifier 64, the second coupled signal 74 as input of the second amplifier 66 may be expressed as −x, i.e., the negative of the first coupled signal of the first amplifier. Accordingly, denote the second coupled signal 74 as −x and denote the second output signal 82 of the second amplifier 66 as y2. Then, the second output signal 82 of the second amplifier 66 can then be approximated as:y2=−a1x+a2x2+−a3x3+a4x4 
The final output signal 84 is formed by combining the two amplifier signals in a second hybrid splitter 68, with a 180-degree phase shift of the second output signal 82 and with 0 degree phase shift of the first output signal 80, effectively subtracting the second output signal 82 from the first output signal 80 to form the final output signal 84, to within a multiplicative constant, 1/√{square root over (2)}, relating to the impedances of the ports, as is well known in the art. Using the foregoing notation, and denoting the final output signal 84 as y3, the final output signal is defined as:       y    3    =                    1                  2                    ⁢              (                              y            1                    -                      y            2                          )              =                  1                  2                    ⁢              (                              2            ⁢                          a              1                        ⁢            x                    +                      2            ⁢                          a              3                        ⁢                          x              3                                      )                            where the multiplicative factor 1/√{square root over (2)} is included for power conservation in the common case where the second hybrid splitter 68 is a passive radio-frequency circuit, and all four ports have the same impedance. The desired linear component of the final output signal 84 is the linear term in the Taylor series expansion, represented in the term 2a1x/√{square root over (2)} in the expression for y3 above. As is well known in the art, the even order distortion terms, or nonlinearities, present in the amplifier output signals y1 and y2, i.e., the a2x2 and a4x4 terms in the Taylor series expansion, are eliminated in the final output signal 84. However, the odd order distortion terms, or nonlinearities, such as the 2a3x3/√{square root over (2)} term in the expression for y3 above, are not eliminated in the final output signal 84. In addition, the method requires two identical amplifiers. Therefore, a need exists to develop methods and apparatus to eliminate odd order nonlinearities, such as the a3x3 and a5x5 terms in the Taylor series expansion of nonlinear circuits, devices, and systems.        
Other prior art approaches use an attenuator or automatic gain control to reduce signal levels, thus resulting in reduction of third-order distortion at a rate faster than reduction of the desired signal levels (due to the cubic term in the Taylor series expansion). See for example, U.S. Pat. No. 4,553,105, Sasaki, issued Nov. 12, 1985; U.S. Pat. No. 5,170,392, Riordan, issued Dec. 8, 1992; U.S. Pat. No. 5,339,454, Kuo et al., issued Aug. 16, 1994; U.S. Pat. No. 5,564,094, Anderson et al., issued Oct. 8, 1996; U.S. Pat. No. 5,697,081, Lyall, Jr. et al., issued Dec. 9, 1997: U.S. Pat. No. 5,758,271, Rich et al., issued May 26, 1998; U.S. Pat. No. 6,044,253, Tsumura, issued Mar. 28, 2000; U.S. Pat. No. 6,052,566, Abramsky et al., issued Apr. 18, 2000; U.S. Pat. No. 6,104,919, and Lyall Jr. et al., issued Aug. 15, 2000. Such approaches employing an attenuator or automatic gain control to reduce signal levels are not generally useful in receiver applications where the attenuation can reduce signal-to-noise ratio of the desired signal, and such approaches are undesirable in transmitter applications where it is desirable for power efficiency purposes to drive the power amplifier at or near the rated output power capacity.
In U.S. Pat. No. 5,917,375, issued on Jun. 29, 1999, in the name of inventors Lisco et al., delay lines and phase shifters are used to produce in-phase desired signals with out-of phase third-order distortion signals, which when added together result in cancellation of the third-order distortion signals. A desired method and apparatus for cancellation of the third-order distortion will eliminate the phase-shift and delay methods taught in the Lisco et al. '375 patent, and will not require the generation of in-phase desired signals components in conjunction with out-of phase third-order distortion signal components.
In other patents; U.S. Pat. No. 5,151,664, issued in the name of inventors Suematsu et al, on Sep. 29, 1992, requires an envelope detection circuit. U.S. Pat. No. 5,237,332, issued in the name of inventors Estrick et al, on Aug. 17, 1993 requires a cubing circuit that generates only the cubic terms of the Taylor series and requires an analog to digital conversion and complex weight and calibration signal. U.S. Pat. No. 5,774,018, issued in the name of inventors Gianfortune et al., on Jun. 30, 1998, requires a predistorter and delay line and is designed for large-signal power amplifier application. Additional methods and apparatus are disclosed in U.S. Pat. No. 5,877,653, issued in the name of inventors Kim et al., on Mar. 2, 1999 that requires predistortion, delay lines, employs the aforementioned variable attenuator methods, and also requires an undistorted reference signal.
Alternate methods and devices are taught in U.S. Pat. No. 5,977,826, issued in the name of inventors Behan et al., on Nov. 2, 1999, which requires a test signal and vector modulator. U.S. Pat. No. 5,994,957, issued in the name of inventor Myer, on Nov. 30, 1999 teaches required delay lines and predistortion circuit. U.S. Pat. No. 6,198,346, issued in the name of inventors Rice et al., on Mar. 6, 2001 requires multiple feedforward loops, delay lines and phase shifters. U.S. Pat. No. 6,208,207, issued in the name of inventor Cavers, on Mar. 27, 2001 requires three parallel signal paths, delay lines, and complex gain adjusters. U.S. Pat. No. 5,051,704, issued in the name of inventors Chapman et al., on Sep. 24, 1991, requires a pilot signal and least means square circuit. U.S. Pat. No. 5,760,646, issued in the name of inventors Belcher et al., requires a predistortion modulator.
Therefore, a need exists to develop methods and apparatus to substantially reduce and/or cancel nonlinearities in circuits, devices, and systems. In particular a desired need exists to reduce, remove, cancel, and eliminate odd order nonlinearities, such as the a3x3 and a5x5 terms in the Taylor series expansion of nonlinear circuits, devices, and systems. This need is especially apparent in radio communication systems such as cellular phones and in other related technical areas. The methods and apparatus should be capable of the necessary function without the need to incorporate delay lines, undistorted reference signals and distortion error signals. Additionally, the means for reducing, canceling, eliminating or enhancing nonlinearities should be able to accomplish such with minimal adverse effect on noise figure and with minimal added noise.
Additionally, a specific need exists to reduce, remove, cancel, and eliminate third order nonlinearities from circuits, devices, and systems, in particular amplifier circuits. Such reduction, removal and cancellation of nonlinear distortions will result in desired high quality amplification of signals. A more general need exists to reduce, remove, cancel, and eliminate any order nonlinearity from circuits, devices, and systems, such as amplifiers, mixers or the like.
Also, in those applications in which nonlinearities are used to achieve desired effects, enhancement of the nonlinearities is desired to improve such devices and systems.
The desired means for reducing, canceling, eliminating and/or enhancing nonlinearities should be cost effective, thus eliminating the need to implement costly high power devices such as amplifiers and mixers to achieve lowered levels of nonlinear distortion. Additionally, the desired means for reducing, canceling, eliminating and/or enhancing nonlinearities should provide for reduced power consumption, thus reducing the high power consumption typically associated with prior art high power devices such as amplifiers and mixers required to achieve lowered levels of nonlinear distortion.
Another desired aspect of the means for reduction, cancellation, elimination and/or enhancement of the nonlinearities is to incorporate an adaptive means of reducing or canceling the nonlinear distortions, wherein the parameters of the methods used to affect reduction, cancellation, elimination or enhancement can be adjusted to effect cancellation of undesired nonlinearities.
A need exists to develop means and methods for reducing or canceling nonlinear distortions in integrated circuit implementations where devices and components used in integrated circuits, such as amplifiers and mixers, can be accurately fabricated so as to effect reduction or cancellation of undesired nonlinearities. Examples of such integrated circuit devices include metal oxide field effect transistors, GaAs field effect transistors, bipolar transistors, diodes, and the like. In particular, if the performance of one integrated circuit device changes from batch-to-batch or from chip-to-chip, the second integrated circuit device, being integrated on the same chip, will typically have performance in track with the first integrated circuit device, preserving the desired reduction or cancellation. As is well known in the art, scaling of devices on integrated circuits can be done accurately, permitting the control of relative parameters of devices and allowing effective integrated circuit implementation.